Inverse radiative transfer with goal-oriented hp-adaptive mesh refinement: adaptive-mesh inversion

Abstract

The inverse problem for radiative transfer is important in many applications, such as optical tomography and remote sensing. Major challenges include large memory requirements and computational expense, which arise from high-dimensionality and the need for iterations in solving the inverse problem. Here, to alleviate these issues, we propose adaptive-mesh inversion: a goal-oriented hp-adaptive mesh refinement (AMR) method for solving inverse radiative transfer problems. One novel aspect here is that the two optimizations (one for inversion, and one for mesh adaptivity) are treated simultaneously and blended together. By exploiting the connection between duality-based mesh adaptivity and adjoint-based inversion techniques, we propose a goal-oriented error estimator, which is cheap to compute, and can efficiently guide the mesh-refinement to numerically solve the inverse problem. We use discontinuous Galerkin spectral element (DGSE) methods to discretize the forward and the adjoint problems. Then, based on the goal-oriented error estimator, we propose an hp-adaptive algorithm to refine the meshes. Numerical experiments are presented at the end and show convergence speed-up and reduced memory occupation by the goal-oriented mesh adaptive method.

A Universal Predictor‐Corrector Approach for Minimizing Artifacts Due To Mesh Refinement

“…(1989), W. C. Skamarock and Klemp (1993), Staniforth (1997), Jablonowski et al. (2006, 2009), Harris and Durran (2010), and Marsico and Stechmann (2020) for weather and climate prediction; Blayo and Debreu (1999) and Debreu and Blayo (2008) for ocean modeling; Evans (1998) and Du and Stechmann (2023a, 2023b, 2023c) for radiative transfer; Berger and Oliger (1984), Berger and Colella (1989), and Bell et al. (1994) for hyperbolic systems and shock waves; and Pelties et al.…”